Problem: $h(x) = -3x^{2}-4x$ $g(n) = 4n^{2}+2(h(n))$ $ g(h(1)) = {?} $
Solution: First, let's solve for the value of the inner function, $h(1)$ . Then we'll know what to plug into the outer function. $h(1) = -3(1^{2})+(-4)(1)$ $h(1) = -7$ Now we know that $h(1) = -7$ . Let's solve for $g(h(1))$ , which is $g(-7)$ $g(-7) = 4(-7)^{2}+2(h(-7))$ To solve for the value of $g$ , we need to solve for the value of $h(-7)$ $h(-7) = -3(-7)^{2}+(-4)(-7)$ $h(-7) = -119$ That means $g(-7) = 4(-7)^{2}+(2)(-119)$ $g(-7) = -42$